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The Math Myth

econlog.econlib.org

281–290 of 328 posts

Re: The Math Myth

#281
post #240

100000% accurate article. It frustrates me when I see even professional programmers perpetuating the "Math Myth", as it's called here. "It's important for all programmers to have a foundation in CS theory!" No, it's not. The vast majority of human beings will never do anything intellectually intensive post-college. Even those in STEM fields. Not that an undergrad degree is "intellectually intensive" anyway. EDIT: >Th…

> The vast majority of human beings will never do anything intellectually intensive post-college

Not true of the people I know or the people who work for me.

Perhaps its true for some-- the idea makes me quite sad.

What a waste.

Re: The Math Myth

#282
Generalizing observations from the lowest common denominator in any work place, at its core this article is very cynical and perhaps wishes everyone would just be happy in their mediocrity.

In most projects, there are minority extra-brilliant people, whose talent/knowledge reflect on the entire outcome/product. So you always need people to handle more complexity. And as some others in the discussion have pointed out, often concepts at a level, become clearer when you grapple the next level of complexity.

Soviet society did not fail because they were better at Maths. It may have happened despite it. The right point to infer about that would be, brilliance in Maths is not a sufficient condition for society as a whole to excel. And that's a moot point, as there are so many other necessary conditions - food/shelter/being-alive/etc - leave aside politics.

Also the article ignores probability as a core life concept, by which you can understand so many things. I use it with my kids all the time.

Another thing which frustrates me recently is my inability to grasp modern physics. Without the relevant understanding of the complex maths, one can only get the vaguest idea, of what they(the physicists) are saying. This creates a huge intellectual gap in society.

Also the knowledge gap has another problem. If it gets too wide, then there will be a very-very few ultra elites who all know what they are saying (perhaps that's already the case, unfortunately). And the rest of us, only take their word on face value. I know one person can't know everything and this is an era of specialization. But still, I think Maths is a fundamental thing. And society would only gain when more number of people are proficient at it.

Re: The Math Myth

#283
post #261
post #232

Earlier quoted context omitted.

> So you're saying a countable infinity can be occupied, so that there is no room for one more. No. I'm saying that a countable infinity doesn't have room for one more at the end . There is no end. You can obviously stick a 1 in the middle, but then you have a number strictly less than 0.999...

You might be able to do something funny with a series whose terms are indexed by ordinals. The last `1` would then be indexed by `omega` (the first transfinite ordinal). I can't claim that the ordinary rules of arithmetic would make much sense, but it's certainly an idea that you can attempt to formalize.

It has been done:

https://en.wikipedia.org/wiki/Infinitesimal

Re: The Math Myth

#284
post #83
post #61

Earlier quoted context omitted.

All mathematics is applied mathematics. Pure mathematics is just mathematics applied to mathematics. This is problematic, because the way mathematics is currently taught only small number of students actually grok it and make deep connections that enable them to build up on what they previously learned and learn more. Others have the constant feeling of things getting progressively harder to understand and use. I'm s…

>> I think it's possible to teach most people to think _in math_ Something like betterexplained.com who tries to develop people's math intuition ?

Thanks so much for sharing https://betterexplained.com. I'm amazed I haven't heard of it before.

Re: The Math Myth

#285

I have relatively little mathematical education and have been seeking to correct that by self-educating over the last year, so I have a certain bias. Nonetheless, I disagree with the key points of this article. The article asserts that most modern professional jobs requires only "Excel" and 8th grade programming. In my experience, over-reliance on software like Excel rather than a basic competency in numerical progra…

What are you using to self-educate? I'm kind of doing the same. I decided to start with "Mathematics for the Nonmathematician", which so far is good (only on chapter 3 though).

Someone in the comments shared https://betterexplained.com/ - which I hadn't heard of and looks great.

Re: The Math Myth

#286
post #182

I studied undergrad CS including the required math department classes. Recently for my Android app ( http://play.google.com/store/apps/details?id=com.unwrappedap... ) I wanted to list the most popular wallpapers. I had a problem though - I was continually adding new wallpapers. How do I compare a new wallpaper which a few people took versus a very old wallpaper which hundreds took? The answer I came up with was N0e^-…

I continually study more sources to improve my competence as a software developer. I have seen too many blunders as elementary as divisions by zero in code and understand that a decent understanding of math and CS aids in writing "better" programs. I have also experienced multiple accounts where my math/CS background, however limited, helped me find the right direction to venture towards. It helped me develop some sense of intuition that is extremely valuable in my line of work. So I will keep on studying.

Re: The Math Myth

#287
post #275

Even if this article were correct that math isn't necessary for employment, it would be wrong that math education is unimportant. It isn't even correct on the employment front, though, because it is attempting to unimaginatively extrapolate from the current state of employment. John Nagle's comment at https://news.ycombinator.com/item?id=12422307 probably expresses this better than I can, but if you're going to make…

The moment we manage to cover the "education gives us control over our impulses" part for a majority of the population, democracy would truly work to our benefit. Although some may not actively rely on whatever they may have learned in a math class, they may still use some of that information to form intuition and subliminally guide them in their thought processes. Engineers who studied or practiced the arts in some portion of their lives may subliminally transfer some of their learnings from that domain into their work as well. Simply arguing that one doesn't need higher math because they don't actively use it is therefore unfair.

Re: The Math Myth

#288
post #217

I was a maths minor and dropped out of a MSc in Applied Maths. I took many courses that would be considered advanced by most, such as Stochastic Calculus, Partial Differential Equations, Multivariate Statistics, Time Series Econometrics, etc. But I left academia over a decade ago, and have never used any of that. I have, however, used a few things above 8th grade maths, such as linear algebra, regression analysis, an…

I use Latin quite frequently to infer the meaning of words in a number of languages including but not limited to English, French, Spanish, Italian and Portuguese. Quite oddly, I'm generally not even aware that I'm inferring meaning of a word by simply studying the roots. In that sense I'm quite grateful for being taught a limited portion of its fundamentals while in high-school. All I am saying is that we may use certain bits of knowledge or certain dormant skills without our awareness to their utilisation.

All of our former experiences help us shape intuition, the same intuition which we may use to make decisions in seemingly unrelated fields. I have therefore become somewhat careful in dismissing a skill, domain of knowledge or lesson for apparent lack of use. The human brain is a fascinating machine; even while we sleep ideas and solutions take shape and who's to say which information is used to form those mental artefacts?

Re: The Math Myth

#289
post #48

Earlier quoted context omitted.

It's not a reduction. If you try to find where to put 0.999... on the number line, it has to go exactly where 1 is. For one thing, 1 - 0.999... = 0.000... because you never get to have any remainder since 0.999... is infinite. Or here's another proof: x = 0.999... 10x = 9.999... 10x - x = 9.999... - 0.999... 9x = 9.000... = 9 9x = 9 x = 1

Your "proofs" simply assumes that 0.999... is a notation denoting 1, without examining the underpinnings which might legitimize that. 9.999.. - 0.999 is 9 no matter how we define .999... just as long as two or more occurrences of the 0.999... notation all denote the same entity, and we understand that the syntax 9.999... is 9 + 0.999... For example, if we define 0.999... as "rubber duck" then 9.999... stands for 9 +…

While that's true, the whole key to the proof is that

0.999... * 10 = 9.999...

Because "one less 9 than infinity is still infinity" it's what really closes the loop on the proof.

Re: The Math Myth

#290
post #128

Earlier quoted context omitted.

The problem with this argument is it assumes you can get to infinity 9s by adding them one-by-one. It's like adding sides to a regular polygon to get to a circle. No matter how many sides you add, you still have a polygon. You can only say that a circle is a polygon with infinity sides, but you'll never get there adding them one by one.

The argument is that you cannot get to infinity by adding one by one. (If the argument assumed otherwise, it would only be temporarily, for the sake of setting up a reductio ad absurdum .)

You can't use induction to get to an infinite amount of nines, so induction doesn't work in this case because you never get there.

The number of nines is not in the set of natural numbers, yet you're trying to use induction by covering every natural number.

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